Finite Group Databasebeta

← Group #13172838

Character table — Group #13172838

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666662333666666666664444366666666666666622446666121212121212121212121212226666666666121212121212121212122244466661212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-11111-1-1111111-1-111111111111111-1-11111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1111-1-11111-1-11111-111-1-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-11111-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-1111111-1-1-111-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-11-1-1-111-1-1-1-111-1-1-1-1-111-1-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-111-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-111111111-1-111111111-1-1-1-1-1-11-1111111-1-1-1-11-11-1-1-1-1111-1-11
χ101111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-111111-1-111-11-11-111-1-1-1-1-111-1
χ111111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-111-1-111-1-11-111-1-1-111-1-1111-1
χ121111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-111-1-11111-1-111-1-1-1-1-1-1-1-11-1-1-111-1111-1-1-1-11111-1-11111111-1-1-11
χ131111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-11-11-111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1111-1-11-1-1-11111-1-111-1-11111111-1-11-1
χ141111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-11-1-111-1-1111-111-1-1-111-1-111-11
χ151111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-111-1-1-11-11-111-1-1-1-1-11-11
χ161111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-111111-1-1-1-1-1-1-1-111-1-1111111111111-11-1-1-1-1-1-111-1-11-11-1-1-1-1111-11-1
χ17222222-12-1-122-122222-1-1-1-12-1-1-1-122-1-12222-12222-1-1-1-1-1-1-1-1-1-1-12200-1-1-1-10022-1-1-1-1002222-1-1-1-122-1-1-1-100-1-1-1-100002000000-1-1000000
χ18222222-12-1-122-122222-1-1-1-12-1-1-1-122-1-122-2-2-12222-1-1-1-1-1-1-1-1-1-1-12-200-1-1110022-1-11100-2-2-2-21111-22-1-11100-1-1110000-200000011000000
χ19222222-12-1-122-122222-1-1-1-12-1-1-1-122-1-1-2-222-12222-1-1-1-1-1-1-1-1-1-1-1-220011-1-100-2-211-1-10022-2-211112-211-1-10011-1-10000-200000011000000
χ20222222-12-1-122-122222-1-1-1-12-1-1-1-122-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-2-200111100-2-2111100-2-222-1-1-1-1-2-2111100111100002000000-1-1000000
χ21222222-12-1-122-1222-22-1-1112-1-1-1-122-1-12222-1-2-2-2-21111-1-1-11111-2-20011110022-1-1-1-1002222-1-1-1-1-2-2111100-1-1-1-10000-200000011000000
χ22222222-12-1-122-1222-22-1-1112-1-1-1-122-1-122-2-2-1-2-2-2-21111-1-1-11111-220011-1-10022-1-11100-2-2-2-211112-211-1-100-1-11100002000000-1-1000000
χ23222222-12-1-122-1222-22-1-1112-1-1-1-122-1-1-2-222-1-2-2-2-21111-1-1-111112-200-1-11100-2-211-1-10022-2-21111-22-1-1110011-1-100002000000-1-1000000
χ24222222-12-1-122-1222-22-1-1112-1-1-1-122-1-1-2-2-2-2-1-2-2-2-21111-1-1-111112200-1-1-1-100-2-2111100-2-222-1-1-1-122-1-1-1-10011110000-200000011000000
χ2522222-12-1222-122-122-12-122-122-1-1-1-12-12200-12-1-1-122-1-1-1-1-1-1-1-1-12022220022-1-12200-1-1000000000-1-1-100-12-1-100-1-1-1-102200-1-10000-1000
χ2622222-12-1222-122-122-12-122-122-1-1-1-12-12200-12-1-1-122-1-1-1-1-1-1-1-1-120-2-22200-2-2-1-1220011000000000-1-1-1001-2-1-10011110-2-2001100001000
χ2722222-12-1222-122-122-12-122-122-1-1-1-12-1-2-200-12-1-1-122-1-1-1-1-1-1-1-1-1-2022-2-2002211-2-200-1-100000000011100-121100-1-1-1-10-2-2001100001000
χ2822222-12-1222-122-122-12-122-122-1-1-1-12-1-2-200-12-1-1-122-1-1-1-1-1-1-1-1-1-20-2-2-2-200-2-211-2-20011000000000111001-21100111102200-1-10000-1000
χ2922222-12-1222-122-12-2-12-1-2-2-122-1-1-1-12-12200-1-2111-2-211-1-1-11111-202-2-2-20022-1-122001100000000011100-1-2-1-100-1-1110-2200110000-1000
χ3022222-12-1222-122-12-2-12-1-2-2-122-1-1-1-12-12200-1-2111-2-211-1-1-11111-20-22-2-200-2-2-1-12200-1-10000000001110012-1-10011-1-102-200-1-100001000
χ3122222-12-1222-122-12-2-12-1-2-2-122-1-1-1-12-1-2-200-1-2111-2-211-1-1-11111202-222002211-2-20011000000000-1-1-100-1-21100-1-11102-200-1-100001000
χ3222222-12-1222-122-12-2-12-1-2-2-122-1-1-1-12-1-2-200-1-2111-2-211-1-1-1111120-222200-2-211-2-200-1-1000000000-1-1-10012110011-1-10-2200110000-1000
χ332222-122222-122-12-12-1-1222-1-1-122-1-1-120022-1-12-1-1-1-122-1-1-1-1-1-1-102220022-1-100002222-1-1000000-1000-1-12-100-1-1-1-1-1-1000220000-1-10-100
χ342222-122222-122-12-12-1-1222-1-1-122-1-1-120022-1-12-1-1-1-122-1-1-1-1-1-1-102-2-2002211000022-2-2-1-1000000-1000-1-1-2100-1-11111000-2-20000110100
χ352222-122222-122-12-12-1-1222-1-1-122-1-1-1200-2-2-1-12-1-1-1-122-1-1-1-1-1-1-10-22200-2-2-1-10000-2-222110000001000112-10011-1-1-1-1000-2-20000110100
χ362222-122222-122-12-12-1-1222-1-1-122-1-1-1200-2-2-1-12-1-1-1-122-1-1-1-1-1-1-10-2-2-200-2-2110000-2-2-2-211000000100011-2100111111000220000-1-10-100
χ372222-122222-122-12-1-2-1-12-2-2-1-1-122-1-1-120022-11-21111-2-2-1-1-111110-22-200-2-2-1-1000022-2-2-1-10000001000112100-1-1-1-111000-220000-1-10100
χ382222-122222-122-12-1-2-1-12-2-2-1-1-122-1-1-120022-11-21111-2-2-1-1-111110-2-2200-2-21100002222-1-1000000100011-2-100-1-111-1-10002-20000110-100
χ392222-122222-122-12-1-2-1-12-2-2-1-1-122-1-1-1200-2-2-11-21111-2-2-1-1-11111022-20022-1-10000-2-2-2-211000000-1000-1-1210011-1-1110002-20000110-100
χ402222-122222-122-12-1-2-1-12-2-2-1-1-122-1-1-1200-2-2-11-21111-2-2-1-1-1111102-220022110000-2-22211000000-1000-1-1-2-1001111-1-1000-220000-1-10100
χ412-22-2222-2-2-2-222-2-22022200-2-2-2-2-22-2222-22-22000000002-2-2000000000000002-22-22-2002-22-222-2-2000000002-22-20000000000000000000
χ422-22-2222-2-2-2-222-2-22022200-2-2-2-2-22-2222-2-222000000002-2-2000000000000002-22-2-2200-22-22-2-222000000002-2-220000000000000000000
χ432-22-2222-2-2-2-222-2-22022200-2-2-2-2-22-222-222-22000000002-2-200000000000000-22-222-2002-2-22-2-22200000000-222-20000000000000000000
χ442-22-2222-2-2-2-222-2-22022200-2-2-2-2-22-222-22-222000000002-2-200000000000000-22-22-2200-222-222-2-200000000-22-220000000000000000000
χ452-22-222-1-211-22-1-2-2202-1-1−i3i3-211112-2-1-12-22-2-10000−i3i3−i3i3-111−i3−i3i3i30000−i3i3−i3i3002-2-11-11002-22-2-1-11100−i3i3−i3i300-11-1100000000000−i3i3000000
χ462-22-222-1-211-22-1-2-2202-1-1−i3i3-211112-2-1-12-2-22-10000−i3i3−i3i3-111−i3−i3i3i30000−i3i3i3−i3002-2-111-100-22-2211-1-100−i3i3i3−i300-111-100000000000i3−i3000000
χ472-22-222-1-211-22-1-2-2202-1-1−i3i3-211112-2-1-1-222-2-10000−i3i3−i3i3-111−i3−i3i3i30000i3−i3−i3i300-221-1-11002-2-2211-1-100i3−i3−i3i3001-1-1100000000000i3−i3000000
χ482-22-222-1-211-22-1-2-2202-1-1−i3i3-211112-2-1-1-22-22-10000−i3i3−i3i3-111−i3−i3i3i30000i3−i3i3−i300-221-11-100-222-2-1-11100i3−i3i3−i3001-11-100000000000−i3i3000000
χ492-22-222-1-211-22-1-2-2202-1-1i3−i3-211112-2-1-12-22-2-10000i3−i3i3−i3-111i3i3−i3−i30000i3−i3i3−i3002-2-11-11002-22-2-1-11100i3−i3i3−i300-11-1100000000000i3−i3000000
χ502-22-222-1-211-22-1-2-2202-1-1i3−i3-211112-2-1-12-2-22-10000i3−i3i3−i3-111i3i3−i3−i30000i3−i3−i3i3002-2-111-100-22-2211-1-100i3−i3−i3i300-111-100000000000−i3i3000000
χ512-22-222-1-211-22-1-2-2202-1-1i3−i3-211112-2-1-1-222-2-10000i3−i3i3−i3-111i3i3−i3−i30000−i3i3i3−i300-221-1-11002-2-2211-1-100−i3i3i3−i3001-1-1100000000000−i3i3000000
χ522-22-222-1-211-22-1-2-2202-1-1i3−i3-211112-2-1-1-22-22-10000i3−i3i3−i3-111i3i3−i3−i30000−i3i3−i3i300-221-11-100-222-2-1-11100−i3i3−i3i3001-11-100000000000i3−i3000000
χ5344444-2-2-2-2-24-2-24-244-2-21-2-2-2-2-211-2-2-21440014-2-2-2-2-21111111114000-2-20000-2-2-2-20000000000000-211000011000000000000000000000
χ5444444-2-2-2-2-24-2-24-244-2-21-2-2-2-2-211-2-2-21-4-40014-2-2-2-2-2111111111-4000220000222200000000000002-1-10000-1-1000000000000000000000
χ5544444-2-2-2-2-24-2-24-24-4-2-2122-2-2-211-2-2-2144001-422222-1-1111-1-1-1-1-4000220000-2-2-2-200000000000002-1-1000011000000000000000000000
χ5644444-2-2-2-2-24-2-24-24-4-2-2122-2-2-211-2-2-21-4-4001-422222-1-1111-1-1-1-14000-2-2000022220000000000000-2110000-1-1000000000000000000000
χ574444-24-24-2-2-24-2-24-24-21-2-2-2-211-2-2-2-21-200441-24-2-211-2-21111111040000-2-2000000-2-200-2-2000000-2000110000110000000000000000000
χ584444-24-24-2-2-24-2-24-24-21-2-2-2-211-2-2-2-21-200-4-41-24-2-211-2-211111110-40000220000002200220000002000-1-10000-1-10000000000000000000
χ594444-24-24-2-2-24-2-24-2-4-21-222-211-2-2-2-21-2004412-422-1-122111-1-1-1-10-4000022000000-2-200-2-20000002000-1-10000110000000000000000000
χ604444-24-24-2-2-24-2-24-2-4-21-222-211-2-2-2-21-200-4-412-422-1-122111-1-1-1-1040000-2-2000000220022000000-2000110000-1-10000000000000000000
χ614444-2-24-244-2-24-2-2-241-2-2441-2-2-2-211-2-200001-2-211-2-2-2-2111111100440000-2-2000000-2-200000000000000-2-200001111000000000000000
χ624444-2-24-244-2-24-2-2-241-2-2441-2-2-2-211-2-200001-2-211-2-2-2-2111111100-4-40000220000002200000000000000220000-1-1-1-1000000000000000
χ634444-2-24-244-2-24-2-2-2-41-2-2-4-41-2-2-2-211-2-20000122-1-12222111-1-1-1-1004-40000-2-20000002200000000000000-22000011-1-1000000000000000
χ644444-2-24-244-2-24-2-2-2-41-2-2-4-41-2-2-2-211-2-20000122-1-12222111-1-1-1-100-44000022000000-2-2000000000000002-20000-1-111000000000000000
χ6544-4-4444-44-44-4-4-44-4044400-44-44-4-44-4-40000400000000-44-40000000000000000000000000000000000000000000000000000000000000
χ6644-4-444-2-4-224-42-44-404-2-200-4-22-22-44220000-2000000002-2200000000000000000000000000−2i32i3−2i32i30000000000000000000000000000000
χ6744-4-444-2-4-224-42-44-404-2-200-4-22-22-44220000-2000000002-22000000000000000000000000002i3−2i32i3−2i30000000000000000000000000000000
χ6844-4-44-2424-442-4-4-2-40-24-20024-4-222-2-420000-2000000002-22000000000000000000000000000000000000000000000000000−2i32i300000000
χ6944-4-44-2424-442-4-4-2-40-24-20024-4-222-2-420000-2000000002-220000000000000000000000000000000000000000000000000002i3−2i300000000
χ7044-4-4-244-44-4-2-4-42420-2-24002-224-42-22-40000-2000000002-22000000000000000000000000000000000000000000000000000000023−230000
χ7144-4-4-244-44-4-2-4-42420-2-24002-224-42-22-40000-2000000002-220000000000000000000000000000000000000000000000000000000−23230000
χ724-44-44-242-4-4-4-24-4240-24-2002-4-422-224-24-400-200000000-22200000000000000-224-400000000000000000000-22000000000000000000000
χ734-44-44-242-4-4-4-24-4240-24-2002-4-422-224-2-4400-200000000-222000000000000002-2-44000000000000000000002-2000000000000000000000
χ744-44-44-2-2222-4-2-2-4240-2-21−2i32i3222-1-1-22-214-40010000−2i32i3i3−i31-1-1i3i3−i3−i30000−2i32i30000-22-2200000000000000i3−i300001-1000000000000000000000
χ754-44-44-2-2222-4-2-2-4240-2-21−2i32i3222-1-1-22-21-440010000−2i32i3i3−i31-1-1i3i3−i3−i300002i3−2i300002-22-200000000000000−i3i30000-11000000000000000000000
χ764-44-44-2-2222-4-2-2-4240-2-212i3−2i3222-1-1-22-214-400100002i3−2i3−i3i31-1-1−i3−i3i3i300002i3−2i30000-22-2200000000000000−i3i300001-1000000000000000000000
χ774-44-44-2-2222-4-2-2-4240-2-212i3−2i3222-1-1-22-21-4400100002i3−2i3−i3i31-1-1−i3−i3i3i30000−2i32i300002-22-200000000000000i3−i30000-11000000000000000000000
χ784-44-4-244-4-4-42442-4-20-2-2400222-4-4-22-24004-4-200000000-2220000000000000000004-400-220000000000000000-220000000000000000000
χ794-44-4-244-4-4-42442-4-20-2-2400222-4-4-22-2400-44-200000000-222000000000000000000-44002-200000000000000002-20000000000000000000
χ804-44-4-24-2-42224-22-4-20-21-2−2i32i32-1-122-221-2004-410000i3−i3−2i32i31-1-1i3i3−i3−i3000000−2i32i3000000-2200-220000000000i3−i300001-10000000000000000000
χ814-44-4-24-2-42224-22-4-20-21-2−2i32i32-1-122-221-200-4410000i3−i3−2i32i31-1-1i3i3−i3−i30000002i3−2i30000002-2002-20000000000−i3i30000-110000000000000000000
χ824-44-4-24-2-42224-22-4-20-21-22i3−2i32-1-122-221-2004-410000−i3i32i3−2i31-1-1−i3−i3i3i30000002i3−2i3000000-2200-220000000000−i3i300001-10000000000000000000
χ834-44-4-24-2-42224-22-4-20-21-22i3−2i32-1-122-221-200-4410000−i3i32i3−2i31-1-1−i3−i3i3i3000000−2i32i30000002-2002-20000000000i3−i30000-110000000000000000000
χ844-4-444444-44-4-4-44-4-40444004-44-44-4-4-4-40000400000000-4-440000000000000000000000000000000000000000000000000000000000000
χ854-4-4444-242-2-4-424-4-404-2-20042-22-2-4-4220000-20000000022-200000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ864-4-4444-242-2-4-424-4-404-2-20042-22-2-4-4220000-20000000022-2000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ874-4-444-24-2-44-42-442-40-24-200-2-442-222-420000-20000000022-20000000000000000000023−23000000000000000000000023−23000000000000000
χ884-4-444-24-2-44-42-442-40-24-200-2-442-222-420000-20000000022-200000000000000000000−23230000000000000000000000−2323000000000000000
χ894-4-44-2444-442-4-4-2-420-2-2400-22-2-44222-40000-20000000022-200000000000023−23000000000000000000000000000023−2300000000000000000
χ904-4-44-2444-442-4-4-2-420-2-2400-22-2-44222-40000-20000000022-2000000000000−23230000000000000000000000000000−232300000000000000000
χ914-4-44-2-24-2-4422-4-22201-2-20012-22-2-1-12200001003-30000-1-113-33-30000000023−2300000023−2300000000000000000000−33−33000000000000000
χ924-4-44-2-24-2-4422-4-22201-2-20012-22-2-1-12200001003-30000-1-113-33-300000000−2323000000−2323000000000000000000003−33−3000000000000000
χ934-4-44-2-24-2-4422-4-22201-2-20012-22-2-1-1220000100-330000-1-11-33-330000000023−23000000−232300000000000000000000−333−3000000000000000
χ944-4-44-2-24-2-4422-4-22201-2-20012-22-2-1-1220000100-330000-1-11-33-3300000000−232300000023−23000000000000000000003−3−33000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-48222-4-42222222220000-1-4-4222222-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4-8222442222222220000-144-2-2-2-2-2-2-1-1-11111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-44-44844-8-4-80-4-42004-442-24-44-20000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-4-8-44-4-844840-42-40042-2-444-4-240000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4848-8-44-84-4402-4-400-2-44-44-22440000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-44-44-4444-44022200-22-22-2-22-2-20000-1000000001-11−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-44-44-4444-44022200-22-22-2-22-2-20000-1000000001-113i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-484-8-84-4844-402-4-400-244442-2-4-400002000000002-2-20000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-44444-4-444-40222−4i34i3-2-2-2-2-22-2220000-100002i3−2i32i3−2i3-111−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44444-4-444-402224i3−4i3-2-2-2-2-22-2220000-10000−2i32i3−2i32i3-111i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1058-8-888-4-4-44-4-84484-80-4-4200-44-4-22444-20000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-484-44-84-4-840-42-400-4-224-444-240000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-44-4444-4440222002-22-22-2-2-2-20000-1006-6000011-1-33-33000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-44-4444-4440222002-22-22-2-2-2-20000-100-66000011-13-33-3000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).